Visual Illusions: Their Causes, Characteristics and Applications

II
THE EYE

The mechanism of the eye makes it possible to see not only light but objects. Elementary eyes of the lowest animals perceive light but cannot see objects. These eyes are merely specialized nerves. In the human eye the optic nerve spreads to form the retina and the latter is a specialized nerve. Nature has accompanied this evolution by developing an instrument the—eye—for intensifying and defining and the whole is the visual sense-organ. The latter contains the most highly specialized nerve and the most refined physiological mechanism, the result being the highest sense-organ.

The eye is approximately a spherical shell transparent at the front portion and opaque (or nearly so) over the remaining eighty per cent of its surface. The optical path consists of a series of transparent liquids and solids. The chief details of the structure of the eye are represented in Fig. 1. Beginning with the exterior and proceeding toward the retina we find in succession the cornea, the anterior chamber containing the aqueous humor, the iris, the lens, the large chamber containing the vitreous humor, and finally the retina. Certain muscles alter the position of the eye and consequently the optical axis, and focusing (accommodation) is accomplished by altering the thickness and shape, and consequently the focal length, of the lens.

The iris is a shutter which automatically controls to some degree the amount of light reaching the retina, thereby tending to protect the latter from too much light. It also has some influence upon the definition of the image; that is, upon what is termed “visual acuity” or the ability to distinguish fine detail. It is interesting to compare the eye with the camera. In the case of the camera and the photographic process, we have (1) an inverted light-image, a facsimile of the object usually diminished in size; (2) an invisible image in the photographic emulsion consisting of molecular changes due to light; and (3) a visible image developed on the plate. In the case of the eye and the visual process we have (1) an inverted light-image, a facsimile of the object diminished in size; (2) the invisible image in the retinal substances probably consisting of molecular changes due to light; and (3) an external visible image. It will be noted that in the case of vision the final image is projected outward—it is external. The more we think of this outward projection the more interesting and marvelous vision becomes. For example, it appears certain that if a photographic plate could see or feel, it would see or feel the silver image upon itself but not out in space. However, this point is discussed further in the next chapter.

In the camera and photographic process we trace mechanism, physics, and chemistry throughout. In the eye and visual process we are able to trace these factors only to a certain point, where we encounter the super-physical and super-chemical. Here molecular change is replaced by sensation, perception, thought, and emotion. Our exploration takes us from the physical world into another, wholly different, where there reigns another order of phenomena. We have passed from the material into the mental world.

The eye as an optical mechanism is reducible to a single lens and therefore the image focused upon the retina is inverted. However, there is no way for the observer to be conscious of this and therefore the inverted image causes no difficulty in seeing. The images of objects in the right half of the field of view are focused upon the left half of the retina. Similarly, the left half of the field of view corresponds to the right half of the retina; the upper half of the former to the lower half of the latter; and so on. When a ray of light from an object strikes the retina the impression is referred back along the ray-line into the original place in space. This is interestingly demonstrated in a simple manner. Punch a pin-hole in a card and hold it about four inches from the eye and at the same time hold a pin-head as close to the cornea as possible. The background for the pin-hole should be the sky or other bright surface. After a brief trial an inverted image of the pin-head is seen in the hole. Punch several holes in the card and in each will be seen an inverted image of the pin-head.

The explanation of the foregoing is not difficult. The pin-head is so close to the eye that the image cannot be focused upon the retina; however, it is in a very favorable position to cast a shadow upon the retina, the light-source being the pin-hole with a bright background. Light streaming through the pin-hole into the eye casts an erect shadow of the pin-head upon the retina, and this erect image is projected into space and inverted in the process by the effect of the lens. The latter is not operative during the casting of the shadow because the pin-head is too close to the lens, as already stated. It is further proved to be outward projection of the retinal image (the shadow) because by multiplying the number of pin-holes (the light-sources) there are also a corresponding number of shadows.

The foregoing not only illustrates the inversion of the image but again emphasizes the fact that we do not see retinal images. Even the “stars” which we see on pressing the eye-lid or on receiving a blow on the eye are projected into space. The “motes” which we see in the visual field while gazing at the sky are defects in the eye-media, and these images are projected into space. We do not see anything in the eye. The retinal image impresses the retina in some definite manner and the impression is carried to the brain by the optic nerve. The intellect then refers or projects this impression outward into space as an external image. The latter would be a facsimile of the physical object if there were no illusions but the fact that there are illusions indicates that errors are introduced somewhere along the path from and to the object.

It is interesting to speculate whether the first visual impression of a new-born babe is “projected outward” or is perceived as in the eye. It is equally futile to conjecture in this manner because there is no indication that the time will come when the baby can answer us immediately upon experiencing its first visual impression. The period of infancy increases with progress up the scale of animal life and this lengthening is doubtless responsible and perhaps necessary for the development of highly specialized sense-organs. Incidentally, suppose a blind person to be absolutely uneducated by transferred experience and that he suddenly became a normal adult and able to see. What would he say about his first visual impression? Apparently such a subject is unobtainable. The nearest that such a case had been approached is the case of a person born blind, whose sight has been restored. This person has acquired much experience with the external world through other senses. It has been recorded that such a person, after sight was restored, appeared to think that external objects “touched” the eyes. Only through visual experience is this error in judgment rectified.

Man studies his kind too much apart from other animals and perhaps either underestimates or overestimates the amount of inherited, innate, instinctive qualities. A new-born chick in a few minutes will walk straight to an object and seize it. Apparently this implies perception of distance and direction and a coördination of muscles for walking and moving the eyes. It appears reasonable to conclude that a certain amount of the wealth of capacities possessed by the individual is partly inherited, and in man the acquired predominates. But all capacities are acquired, for even the inherited was acquired in ancestral experience. Even instinct (whatever that may be) must involve inherited experience. These glimpses of the depths to which one must dig if he is to unearth the complete explanations of visual perception—and consequently of illusions—indicate the futility of treating the theories in the available space without encroaching unduly upon the aims of this volume.

Certain defects of the optical system of the eye must contribute toward causing illusions. Any perfect lens of homogeneous material has at least two defects, known as spherical and chromatic aberration. The former manifests itself by the bending of straight lines and is usually demonstrated by forming an image of an object such as a wire mesh or checkerboard; the outer lines of the image are found to be very much bent. This defect in the eye-lens is somewhat counteracted by a variable optical density, increasing from the outer to the central portion. This results in an increase in refractive-index as the center of the lens is approached and tends to diminish its spherical aberration. The eye commonly possesses abnormalities such as astigmatism and eccentricity of the optical elements. All these contribute toward the creation of illusions.

White light consists of rays of light of various colors and these are separated by means of a prism because the refractive-index of the prism differs for lights of different color or wave-length. This causes the blue rays, for example, to be bent more than the red rays when traversing a prism. It is in this manner that the spectrum of light may be obtained. A lens may be considered to be a prism of revolution and it thus becomes evident that the blue rays will be brought to a focus at a lesser distance than the red rays; that is, the former are bent more from their original path than the latter. This defect of lenses is known as chromatic aberration and is quite obvious in the eye. It may be demonstrated by any simple lens, for the image of the sun, for example, will appear to have a colored fringe. A purple filter which transmits only the violet and red rays is useful for this demonstration. By looking at a lamp-filament or candle-flame some distance away the object will appear to have a violet halo, but the color of the fringe will vary with accommodation. On looking through a pin-hole at the edge of an object silhouetted against the bright sky the edge will appear red if the light from the pin-hole enters the pupil near its periphery. This optical defect of the eye makes objects appear more sharply defined when viewed in monochromatic light. In fact, this is quite obvious when using yellow glasses. The defect is also demonstrated by viewing a line-spectrum focused on a ground glass. The blue and red lines cannot be seen distinctly at the same distance. The blue lines can be focused at a much less distance than the red lines. Chromatic aberration can account for such an illusion as the familiar “advancing” and “retiring” colors and doubtless it plays a part in many illusions.

The structure of the retina plays a very important part in vision and accounts for various illusions and many interesting visual phenomena. The optic nerve spreads out to form the retina which constitutes the inner portion of the spherical shell of the eye with the exception of the front part. Referring again to Fig. 1, the outer coating of the shell is called the sclerotic. This consists of dense fibrous tissue known as the “white of the eye.” Inside this coating is a layer of black pigment cells termed the choroid. Next is the bacillary layer which lines about five-sixths of the interior surface of the eye. This is formed by closely packed “rods” and “cones,” which play a dominant role in the visual process. A light-sensitive liquid (visual purple) and cellular and fibrous layers complete the retinal structure.

The place where the optic nerve enters the eye-ball and begins to spread out is blind. Objects whose images fall on this spot are invisible. This blind-spot is not particularly of interest here, but it may be of interest to note its effect. This is easily done by closing one eye and looking directly at one of two small black circles about two inches apart on white paper at a distance of about a foot from the eye. By moving the objects about until the image of the circle not directly looked at falls upon the blind-spot, this circle will disappear. A three-foot circle at a distance of 36 feet will completely disappear if its image falls directly upon the blind-spot. At a distance of 42 inches the invisible area is about 12 inches from the point of sight and about 3 to 4 inches in diameter. At 300 feet the area is about 8 feet in diameter. The actual size of the retinal blind-spot is about 0.05 inch in diameter or nearly 5 degrees. Binocular vision overcomes any annoyance due to the blind-spots because they do not overlap in the visual field. A one-eyed person is really totally blind for this portion of the retina or of the visual field.

The bacillary layer consists of so-called rods and cones. Only the rods function under very low intensities of illumination of the order of moonlight. The cones are sensitive to color and function only at intensities greater than what may be termed twilight intensities. These elements are very small but the fact that they appear to be connecting links between the retinal image and visual perception, acuity or discrimination of fine detail is limited inasmuch as the elements are of finite dimensions. The smallest image which will produce a visual impression is the size of the end of a cone. The smallest distance between two points which is visible at five inches is about 0.001 inch. Two cones must be stimulated in such a case. Fine lines may appear crooked because of the irregular disposition of these elemental light-sensitive points. This apparent crookedness of lines is an illusion which is directly due to the limitations of retinal elements of finite size.

The distribution of rods and cones over the retina is very important. In the fovea centralis—the point of the retina on the optical axis of the eye—is a slight depression much thinner than the remainder of the retina and this is inhabited chiefly by cones. It is this spot which provides visual acuteness. It is easily demonstrated that fine detail cannot be seen well defined outside this central portion of the visual field. When we desire to see an object distinctly we habitually turn the head so that the image of the object falls upon the fovea of each eye. Helmholtz has compared the foveal and lateral images with a finished drawing and a rough sketch respectively.

The fovea also contains a yellow pigmentation which makes this area of the retina selective as to color-vision. On viewing certain colors a difference in color of this central portion of the field is often very evident. In the outlying regions of the retina, rods predominate and in the intermediate zone both rods and cones are found. Inasmuch as rods are not sensitive to color and cones do not function at low intensities of illumination it is obvious that visual impressions should vary, depending upon the area of the retina stimulated. In fact, many interesting illusions are accounted for in this manner, some of which are discussed later.

It is well known that a faint star is seen best by averted vision. It may be quite invisible when the eye is directed toward it, that is, when its image falls upon the rod-free fovea. However, by averting the line of sight slightly, the image is caused to fall on a retinal area containing rods (sensitive to feeble light) and the star may be readily recognized. The fovea is the point of distinct focus. It is necessary for fixed thoughtful attention. It exists in the retina of man and of higher monkeys but it quickly disappears as we pass down the scale of animal life. It may be necessary for the safety of the lower animals that they see equally well over a large field; however, it appears advantageous that man give fixed and undivided attention to the object looked at. Man does not need to trust solely to his senses to protect himself from dangers. He uses his intellect to invent and to construct artificial defenses. Without the highly specialized fovea we might see equally well over the whole retina but could not look attentively at anything, and therefore could not observe thoughtfully.

When an image of a bright object exists upon the retina for a time there results a partial exhaustion or fatigue of the retinal processes with a result that an after-image is seen. This after-image may be bright for a time owing to the fact that it takes time for the retinal process to die out. Then there comes a reaction which is apparent when the eye is directed toward illuminated surfaces. The part of the retina which has been fatigued does not respond as fully as the fresher areas, with the result that the fatigued area contributes a darker area in the visual field. This is known as an after-image and there are many interesting variations.

The after-image usually undergoes a series of changes in color as well as in brightness as the retinal process readjusts itself. An after-image of a colored object may often appear of a color complementary to the color of the object. This is generally accounted for by fatigue of the retinal process. There are many conflicting theories of color-vision but they are not as conflicting in respect to the aspect of fatigue as in some other aspects. If the eye is directed toward a green surface for a time and then turned toward a white surface, the fatigue to green light diminishes the extent of response to the green rays in the light reflected by the white surface. The result is the perception of a certain area of the white surface (corresponding to the portion of the field fatigued by green light) as of a color equal to white minus some green—the result of which is pink or purple. This is easily understood by referring to the principles of color-mixture. Red, green, and blue (or violet) mixed in proper proportions will produce any color or tint and even white. Thus these may be considered to be the components of white light. Hence if the retina through fatigue is unable to respond fully to the green component, the result may be expressed mathematically as red plus blue plus reduced green, or synthetically a purplish white or pink. When fatigued to red light the after-image on a white surface is blue-green. When fatigued to blue light it is yellowish.

Further mixtures may be obtained by directing the after-image upon colored surfaces. In this manner many of the interesting visual phenomena and illusions associated with the viewing of colors are accounted for. The influence of a colored environment upon a colored object is really very great. This is known as simultaneous contrast. The influence of the immediately previous history of the retina upon the perception of colored surfaces is also very striking. This is called successive contrast. It is interesting to note that an after-image produced by looking at a bright light-source, for example, is projected into space even with the eyes closed. It is instructive to study after-images and this may be done at any moment. On gazing at the sun for an instant and then looking away, an after-image is seen which passes in color from green, blue, purple, etc., and finally fades. For a time it is brighter than the background which may conveniently be the sky. On closing the eyes and placing the hands over them the background now is dark and the appearance of the after-image changes markedly. There are many kinds, effects, and variations of after-images, some of which are discussed in other chapters.

As the intensity of illumination of a landscape, for example, decreases toward twilight, the retina diminishes in sensibility to the rays of longer wave-lengths such as yellow, orange, and red. Therefore, it becomes relatively more sensitive to the rays of shorter wave-length such as green, blue, and violet. The effects of this Purkinje phenomenon (named after the discoverer) may be added to the class of illusions treated in this book. It is interesting to note in this connection that moonlight is represented on some paintings and especially on the stage as greenish blue in color, notwithstanding that physical measurements show it to be approximately the color of sunlight. In fact, it is sunlight reflected by dead, frigid, and practically colorless matter.

Some illusions may be directly traced to the structure of the eye under unusual lighting conditions. For example, in a dark room hold a lamp obliquely outward but near one eye (the other being closed and shielded) and forward sufficiently for the retina to be strongly illuminated. Move the lamp gently while gazing at a plain dark surface such as the wall. Finally the visual field appears dark, due to the intense illumination of the retina and there will appear, apparently projected upon the wall, an image resembling a branching leafless tree. These are really shadows of the blood vessels in the retina. The experiment is more successful if an image of a bright light-source is focused on the sclerotic near the cornea. If this image of the light-source is moved, the tree-like image seen in the visual field will also move.

The rate of growth and decay of various color-sensations varies considerably. By taking advantage of this fact many illusions can be produced. In fact, the careful observer will encounter many illusions which may be readily accounted for in this manner.

It may be said that in general the eyes are never at rest. Involuntary eye-movements are taking place all the time, at least during consciousness. Some have given this restlessness a major part in the process of vision but aside from the correctness of theories involving eye-movements, it is a fact that they are responsible for certain illusions. On a star-lit night if one lies down and looks up at a star the latter will be seen to appear to be swimming about more or less jerkily. On viewing a rapidly revolving wheel of an automobile as it proceeds down the street, occasionally it will be seen to cease revolving momentarily. These apparently are accounted for by involuntary eye-movements which take place regardless of the effort made to fixate vision.

If the eyelids are almost closed, streamers appear to radiate in various directions from a light-source. Movements of the eyelids when nearly closed sometimes cause objects to appear to move. These may be accounted for perhaps by the distortion of the moist film which covers the cornea.

The foregoing are only a few of the many visual phenomena due largely to the structure of the eye. The effects of these and many others enter into visual illusions, as will be seen here and there throughout the chapters which follow.

III
VISION

The sense of sight differs considerably from the other senses. The sense of touch requires solid contact (usually); taste involves liquid contact; smell, gaseous contact; and hearing depends upon a relay of vibrations from an object through another medium (usually air), resulting finally in contact. However, we perceive things at a distance through vibration (electromagnetic waves called light) conveyed by a subtle, intangible, universal medium which is unrecognizable excepting as a hypothetically necessary bearer of light-waves or, more generally, radiant energy.

It also is interesting to compare the subjectiveness and objectiveness of sensations. The sensation of taste is subjective; it is in us, not in the body tasted. In smell we perceive the sensation in the nose and by experience refer it to an object at a distance. The sensation of hearing is objective; that is, we refer the cause to an object so completely that there is practically no consciousness of sensation in the ear. In sight the impression is so completely projected outward into space and there is so little consciousness of any occurrence in the eye that it is extremely difficult to convince ourselves that it is essentially a subjective sensation. The foregoing order represents the sense-organs in increasing specialization and refinement. In the two higher senses—sight and hearing—there is no direct contact with the object and an intricate mechanism is placed in front of the specialized nerve to define and to intensify the impression. In the case of vision this highly developed instrument makes it possible to see not only light but objects.

As we go up the scale of vertebrate animals we find that there is a gradual change of the position of the eyes from the sides to the front of the head and a change of the inclination of the optical axes of the two eyes from 180 degrees to parallel. There is also evident a gradual increase in the fineness of the bacillary layer of the retina from the margins toward the center, and, therefore, an increasing accuracy in the perception of form. This finally results in a highly organized central spot or fovea which is possessed only by man and the higher monkeys. Proceeding up the scale we also find an increasing ability to converge the optic axes on a near point so that the images of the point may coincide with the central spots of both retinas. These changes and others are closely associated with each other and especially with the development of the higher faculties of the mind.

Binocular vision in man and in the higher animals is the last result of the gradual improvement of the most refined sense-organ, adapting it to meet the requirements of highly complex organisms. It cannot exist in some animals, such as birds and fishes, because they cannot converge their two optical axes upon a near point. When a chicken wishes to look intently at an object it turns its head and looks with one eye. Such an animal sees with two eyes independently and possibly moves them independently. The normal position of the axes of human eyes is convergent or parallel but it is possible to diverge the axes. In fact, with practice it is possible to diverge the axes sufficiently to look at a point near the back of the head, although, of course, we do not see the point.

The movement of the eyes is rather complex. When they move together to one side or the other or up and down in a vertical plane there is no rotation of the optical axes; that is, no torsion. When the visual plane is elevated and the eyes move to the right they rotate to the right; when they move to the left they rotate to the left. When the visual plane is depressed and the eyes move to the right they rotate to the left; when they move to the left they rotate to the right. Through experience we unconsciously evaluate the muscular stresses, efforts, and movements accompanying the motion of the eyes and thereby interpret much through visual perception in regard to such aspects of the external world as size, shape, and distance of objects. Even this brief glimpse of the principal movements of the eyes indicates a complexity which suggests the intricacy of the explanations of certain visual phenomena.

At this point it appears advantageous to set down the principal modes by which we perceive the third dimension of space and of objects and other aspects of the external world. They are as follows: (1) extent; (2) clearness of brightness and color as affected by distance; (3) interference of near objects with those more distant; (4) elevation of objects; (5) variation of light and shade on objects; (6) cast shadows; (7) perspective; (8) variation of the visor angle in proportion to distance; (9) muscular effort attending accommodation of the eye; (10) stereoscopic vision; (11) muscular effort attending convergence of the axes of the eyes. It will be recognized that only the last two are necessarily concerned with binocular vision. These varieties of experiences may be combined in almost an infinite variety of proportions.

Wundt in his attempt to explain visual perception considered chiefly three factors: (1) the retinal image of the eye at rest; (2) the influence of the movements of one eye; and, (3) the additional data furnished by the two eyes functioning together. There are three fields of vision corresponding to the foregoing. These are the retinal field of vision, the monocular field, and the binocular field. The retinal field of vision is that of an eye at rest as compared with the monocular field, which is all that can be seen with one eye in its entire range of movement and therefore of experience. The retinal field has no clearly defined boundaries because it finally fades at its indefinite periphery into a region where sensation ceases.

It might be tiresome to follow detailed analyses of the many modes by which visual perception is attained, so only a few generalizations will be presented. For every voluntary act of sight there are two adjustments of the eyes, namely, focal and axial. In the former case the ciliary muscle adjusts the lens in order to produce a defined image upon the retina. In axial adjustments the two eyes are turned by certain muscles so that their axes meet on the object looked at and the images of the object fall on the central-spots of the retina. These take place together without distinct volition for each but by the single voluntary act of looking. Through experience the intellect has acquired a wonderful capacity to interpret such factors as size, form, and distance in terms of the muscular movements in general without the observer being conscious of such interpretations.

Binocular vision is easily recognized by holding a finger before the eyes and looking at a point beyond it. The result is two apparently transparent fingers. An object is seen single when the two retinal images fall on corresponding points. Direction is a primary datum of sense. The property of corresponding points of the two retinas (binocular vision) and consequently of identical spatial points in the two visual fields is not so simple. It is still a question whether corresponding points (that is, the existence of a corresponding point in one retina for each point in the other retina) are innate, instinctive, and are antecedent of experience or are “paired” as the result of experience. The one view results in the nativistic, the other in the empiristic theory. Inasmuch as some scientists are arrayed on one side and some on the other, it appears futile to dwell further upon this aspect. It must suffice to state that binocular vision, which consists of two retinas and consequently two fields of view absolutely coördinated in some manner in the brain, yields extensive information concerning space and its contents.

After noting after-images, motes floating in the field of view (caused by defects in the eye-media) and various other things, it is evident that what we call the field of view is the external projection into space of retinal states. All the variations of the latter, such as images and shadows which are produced in the external field of one eye, are faithfully reproduced in the external field of the other eye. This sense of an external visual field is ineradicable. Even when the eyes are closed the external field is still there; the imagination or intellect projects it outward. Objects at different distances cannot be seen distinctly at the same time but by interpreting the eye-movements as the point of sight is run backward and forward (varying convergence of the axes) the intellect practically automatically appraises the size, form, and distance of each object. Obviously, experience is a prominent factor. The perception of the third dimension, depth or relative distance, whether in a single object or a group of objects, is the result of the successive combination of the different parts of two dissimilar images of the object or group.

As already stated, the perception of distance, size, and form is based partly upon monocular and partly upon binocular vision, and the simple elements upon which judgments of these are based are light, shade, color, intensity, and direction. Although the interpretation of muscular adjustments plays a prominent part in the formation of judgments, the influences of mathematical perspective, light, shade, color, and intensity are more direct. Judgments based upon focal adjustment (monocular) are fairly accurate at distances from five inches to several yards. Those founded upon axial adjustment (convergence of the two axes in binocular vision) are less in error than the preceding ones. They are reliable to a distance of about 1000 feet. Judgments involving mathematical perspective are of relatively great accuracy without limits. Those arrived at by interpreting aerial perspective (haziness of atmosphere, reduction in color due to atmospheric absorption, etc.) are merely estimates liable to large errors, the accuracy depending largely upon experience with local conditions.

The measuring power of the eye is more liable to error when the distances or the objects compared lie in different directions. A special case is the comparison of a vertical distance with a horizontal one. It is not uncommon to estimate a vertical distance as much as 25 per cent greater than an actually equal horizontal distance. In general, estimates of direction and distance are comparatively inaccurate when only one eye is used although a one-eyed person acquires unusual ability through a keener experience whetted by necessity. A vertical line drawn perpendicular to a horizontal one is likely to appear bent when viewed with one eye. Its apparent inclination is variable but has been found to vary from one to three degrees. Monocular vision is likely to cause straight lines to appear crooked, although the “crookedness” may seem to be more or less unstable.

The error in the estimate of size is in reality an error in the estimation of distance except in those cases where the estimate is based directly upon a comparison with an object of supposedly known size. An amusing incident is told of an old negro who was hunting for squirrels. He shot several times at what he supposed to be a squirrel upon a tree-trunk and his failure to make a kill was beginning to weaken his rather ample opinion of his skill as a marksman. A complete shattering of his faith in his skill was only escaped by the discovery that the “squirrel” was a louse upon his eyebrow. Similarly, a gnat in the air might appear to be an airplane under certain favorable circumstances. It is interesting to note that the estimated size of the disk of the sun or moon varies from the size of a saucer to that of the end of a barrel, although a pine tree at the horizon-line may be estimated as 25 feet across despite the fact that it may be entirely included in the disk of the sun setting behind it.

Double images play an important part in the comparison of distances of objects. The “doubling” of objects is only equal to the interocular distance. Suppose two horizontal wires or clotheslines about fifty feet away and one a few feet beyond the other. On looking at these no double images are visible and it is difficult or even impossible to see which is the nearer when the points of attachment of the ends are screened from view. However, if the head is turned to one side and downward (90 degrees) so that the interocular line is now at right angles (vertical) to the horizontal lines, the relative distances of the latter are brought out distinctly. Double images become visible in the latter case.

According to Brücke’s theory the eyes are continuously in motion and the observer by alternately increasing or decreasing the convergence of the axes of the eyes, combines successively the different parts of the two scenes as seen by the two eyes and by running the point of sight back and forth by trial obtains a distinct perception of binocular perspective or relief or depth of space. It may be assumed that experience has made the observer proficient in this appraisal which he arrives at almost unconsciously, although it may be just as easy to accept Wheatstone’s explanation. In fact, some experiences with the stereoscope appear to support the latter theory.

Wheatstone discovered that the dissimilar pictures of an object or scene, when united by means of optical systems, produce a visual effect similar to that produced by the actual solid object or scene provided the dissimilarity is the same as that between two retinal images of the solid object or scene. This is the principle upon which the familiar stereoscope is founded. Wheatstone formulated a theory which may be briefly stated as follows: In viewing a solid object or a scene two slightly dissimilar retinal images are formed in the two eyes respectively, but the mind completely fuses them into one “mental” image. When this mental fusion of the two really dissimilar retinal images is complete in this way, it is obvious that there cannot exist a mathematical coincidence. The result is a perception of depth of space, of solidity, of relief. In fact the third dimension is perceived. A stereoscope accomplishes this in essentially the same manner, for two pictures, taken from two different positions respectively corresponding to the positions of the eyes, are combined by means of optical systems into one image.

Lack of correct size and position of the individual elements of stereoscopic pictures are easily detected on combining them. That is, their dissimilarity must exactly correspond to that between two views of an object or scene from the positions of the two eyes respectively (Fig. 2). This fact has been made use of in detecting counterfeit notes. If two notes made from the same plate are viewed in a stereoscope and the identical figures are combined, the combination is perfect and the plane of the combined images is perfectly flat. If the notes are not made from the same plate but one of them is counterfeit, slight variations in the latter are unavoidable. Such variations will show themselves in a wavy surface.

The unwillingness of the visual sense to combine the two retinal images, if they are dissimilar to the extent of belonging to two different objects, is emphasized by means of colors. For example, if a green glass is placed over one eye and a red glass over the other, the colors are not mixed by the visual sense. The addition of these two colors results normally in yellow, with little or no suggestion of the components—red and green. But in the foregoing case the visual field does not appear of a uniform yellow. It appears alternately red and green, as though the colors were rivaling each other for complete mastery. In fact, this phenomenon has been termed “retinal rivalry.”

The lenses of the stereoscope supplement eye-lenses and project on the retina two perfect images of a near object, although the eyes are looking at a distant object and are therefore not accommodated for the near one (the photographs). The lenses enlarge the images similar to the action of a perspective glass. This completes the illusion of an object or of a scene. There is a remarkable distinctness of the perception of depth of space and therefore a wonderful resemblance to the actual object or scene. It is interesting to note the effect of taking the two original photographs from distances separated by several feet. The effect is apparently to magnify depth. It is noteworthy that two pictures taken from an airplane at points fifty feet or so apart, when combined in the stereoscope, so magnify the depth that certain enemy-works can be more advantageously detected than from ordinary photographs.

Stereoscopic images such as represented in Fig. 2 may be combined without the aid of the stereoscope if the optical axes of the eye can be sufficiently converged or diverged. Such images or pictures are usually upon a card and are intended to be combined beyond the plane of the card, for it is in this position that the object or scene can be perceived in natural perspective, of natural size, of natural form, and at natural distance. But in combining them the eyes are looking at a distant object and the axes are parallel or nearly so. Therefore, the eyes are focally adjusted for a distant object but the light comes from a very near object—the pictures on the card. Myopic eyes do not experience this difficulty and it appears that normal vision may be trained to overcome it. Normal eyes are aided by using slightly convex lenses. Such glasses supplement the lenses of the eye, making possible a clear vision of a near object while the eyes are really looking far away or, in other words, making possible a clear image of a near object upon the retina of the unadjusted eye. Stereoscopic pictures are usually so mounted that “identical points” on the two pictures are farther apart than the interocular distance and therefore the two images cannot be combined when the optical axes of the eyes are parallel or nearly so, which is the condition when looking at a distant object. In such a case the two pictures must be brought closer together.

Fig. 2.—Stereoscopic pictures for combining by converging or diverging the optical axes.

In Figs. 2 and 3 are found “dissimilar” drawings of the correct dissimilarity of stereoscopic pictures. It is interesting and instructive to practice combining these with the unaided eyes. If Fig. 2 is held at an arm’s length and the eyes are focused upon a point several inches distant, the axes will be sufficiently converged so that the two images are superposed. It may help to focus the eyes upon the tip of a finger until the stereoscopic images are combined. In this case of converging axes the final combined result will be the appearance of a hollow tube or of a shell of a truncated cone, apparently possessing the third dimension and being perceived as apparently smaller than the actual pictures in the background at arm’s length. If the two stereoscopic pictures are combined by looking at a point far beyond the actual position of Fig. 2, the combined effect is a solid truncated cone but perceived as of about the same size and at about the same distance from the eye as the actual diagrams. In the latter case the smaller end of the apparent solid appears to be nearer than the larger end, but in the former case the reverse is true, that is, the smaller end appears to be at a greater distance. The same experiments may be performed for Fig. 3 with similar results excepting that this appears to be a shell under the same circumstances that Fig. 2 appears to be a solid and vice versa. A few patient trials should be rewarded by success, and if so the reader can gain much more understanding from the actual experiences than from description.

The foregoing discussion of vision should indicate the complexity of the visual and mental activities involved in the discrimination, association, and interpretation of the data obtained through the eye. The psychology of visual perception is still a much controverted domain but it is believed that the glimpses of the process of vision which have been afforded are sufficient to enable the reader to understand many illusions and at least to appreciate more fully those whose explanations remain in doubt. Certainly these glimpses and a knowledge of the information which visual perception actually supplies to us at any moment should convince us that the visual sense has acquired an incomparable facility for interpreting the objective world for us. Clearness of vision is confined to a small area about the point of sight, and it rapidly diminishes away from this point, images becoming dim and double. We sweep this point of sight backward and forward and over an extensive field of view, gathering all the distinct impressions into one mental image. In doing this the unconscious interpretation of the muscular activity attending accommodation and convergence of the eyes aids in giving to this mental picture the appearance of depth by establishing relative distances of various objects. Certainly the acquired facility is remarkable.

IV
SOME TYPES OF GEOMETRICAL ILLUSIONS

The Effect of the Location in the Visual Field.—One of the most common illusions is found in the letter “S” or figure “8.” Ordinarily we are not strongly conscious of a difference in the size of the upper and lower parts of these characters; however, if we invert them the difference is seen to be large. The question arises, Is the difference due fundamentally to the locations of the two parts in the visual field? It scarcely seems credible that visual perception innately appraises the upper part larger than the lower, or the lower smaller than the upper part when these small characters are seen in their accustomed position. It appears to be possible that here we have examples of the effect of learning or experience and that our adaptive visual sense has become accustomed to overlook the actual difference. That is, for some reason through being confronted with this difference so many times, the intellect has become adapted to it and, therefore, has grown to ignore it. Regardless of the explanation, the illusion exists and this is the point of chief interest. For the same reason the curvature of the retina does not appear to account for illusion through distortion of the image, because the training due to experience has caused greater difficulties than this to disappear. We must not overlook the tremendous “corrective” influence of experience upon which visual perception for the adult is founded. If we have learned to “correct” in some cases, why not in all cases which we have encountered quite generally?